For what value of k for which the roots of the quadratic equation 9x² 3kx +K 0 has real and equal roots?.

Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Probabilities can be expressed using the numbers 0 , 1, fractions with just a range of 0% - 100%, or an another few characters. the proportion of occurrences among a group of equally likely options out of all conceivable outcomes.

Here,

Given :

In a game, Rachel has the option of picking any one of three cards at random. She will receive $10 if she chooses Card A.

Choosing Card B will earn her $15.

She will receive $50 if she chooses Card C.

Thus ,

expected value of winning is $10 which is the least prize that is $10 on selected card A.

As the probability is 1/3 = 0.33

Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.

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Answer:

Step-by-step explanation:

$25

To write 300000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.

300000000 in standard form would be written as 3 x 10^8.

To arrive at this form, we move the decimal point 8 places to the left (since there are 8 zeros in 300000000) and add the power of 10 notation, indicating that we moved the decimal point 8 places to the left. The number 3 is the coefficient and 8 is the exponent. This way, we get 3 x 10^8 which is the standard form of 300000000.

Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers.

When a number is written in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10.

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If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

We have to prove that ∠A + ∠B + ∠C is equal to 180 degrees.

The measure of A = ∠1

B = ∠2

C = ∠3

Given, l || BC

We know that the alternate angles are equal in parallel lines.

∠2 = ∠4 -------------- (1)

∠3 = ∠5 -------------- (2)

Adding (1) and (2),

∠2 + ∠3 = ∠4 + ∠5

By adding ∠1 on both sides,

∠1 + ∠2 + ∠3 = ∠4 + ∠5 + ∠1

From the figure,

The sum of the angles at a point on a line is equal to 180 degrees.

∠4 + ∠1 + ∠5 = 180°

So, ∠1 + ∠2 + ∠3 = 180°

Therefore, ∠A + ∠B + ∠C = 180°

Thus, If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.

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The angle that are equal to m∠5 are ∠9 and ∠12, therefore, C and D.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

As per the given image, the two streets 1st ave and 2nd ave are parallel to each other while D street acts as a transverse and intersects both 1st ave and 2nd ave. Therefore, the angle that will be equal to m∠5 are:

m∠5 = m∠9, Becuase the two angles are the corresponding angles

m∠5 = m∠9m = m∠12, Becuase ∠9 and ∠12 are vertically opposite angles.

Hence, the correct options are C and D.

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Answer:

327 miles

Step-by-step explanation:

Answer:

327.5 miles

Step-by-step explanation:

45 times 4.5 + 50 times 2.5 = 327.5

The equivalent expression is -4m -2

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.

These algebraic expressions are also known to consist of some arithmetic operations, such as;

From the information given, we have that;

4m−2+(−8m)

Now, expand the bracket

4m - 2 - 8m

Collect like terms, we get;

4m - 8m - 2

Subtract the like terms

-4m - 2

Hence, the expression is -4m - 2

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Answer:  y=17.3

refer to the image for the steps

Time after 220 minutes will be 6:40 on the clock.

Add 60 minutes to the end minutes and take an hour off the end time hours if the start minutes are greater than the end minutes. Subtract the start time minutes from the final minutes as you go. Add the hours from the start to the end. To find the solution, combine the results for hours and minutes.

1 hour = 60 mins

220 minutes = hours?

⇒ 220 / 60

⇒ 3 4/6

⇒ 3 hours and 40 minutes

At present, it's 3:00,

The time after 220 minutes will be -

⇒ 3 + 3.7 hours

⇒ 6.7 hours

The clock will show time 6: 40.

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Answer:

m = 0.28

Step-by-step explanation:

you can create a proportion as follows:

[tex]\frac{2.8}{m}[/tex] = [tex]\frac{4}{5.4}[/tex]

cross-multiply to get:

4m = 2.8(5.4)

4m = 15.12

m = 15.12/4

m = 3.78

Answer:

m = 3.78

Step-by-step explanation:

Find the factor of how much bigger the second triangle is:

5.4 - 4 = 1.4

1.4/4 = 0.35

Then, multiply it by the top side

0.35 x 2.8 = 0.98

Finally, add the top number and the product

0.98 + 2.8 = 3.78

There is your answer!

The process of find the x and y coordinates of the vertex of a parabola is y = -b/2a

Coordinates in math is known as  a number on the x-axis called an x-coordinate and a number on the y-axis called a y-coordinate.

Here we need to write down the process of finding the x and y coordinates of the vertex of a parabola.

The first step is to Get the equation in the form y = ax² + bx + c.

And then we have to calculate -b / 2a ad this is the x-coordinate of the vertex.

In order to find the y-coordinate of the vertex, then we have to simply plug the value of -b / 2a into the equation for x and solve for y.

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I would be paid $310.4 for 32 hour of work at the same rate

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

We transform the mixed fraction into improper fraction and we have:

24 1/2 =

[(24*2) + 1)] /2=

[48+1] /2=

49/2

Calculating the amount of dollars paid for 1 hour worked:

Dollar per hour = Paid  / Hours worked

Dollar per hour = $236.64 / (49/2)

Dollar per hour = $236.64 * 2 / 49

Dollar per hour = $473.28/49

Dollar per hour = $9.70

Calculating the amount of dollars paid for 32 hours worked:

Paid (32h) = Dollar per hour * Hours

Paid (32h) = $9.70/h * 32 h

Paid (32h) = $310.4

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The lengths of all three sides of the triangle are;

43.6 inches

52.3 inches

61.1 inches

The arcs are seen to be two times the angles and as such, the arc made by the 50° angle is 100° and then we see that the one made by the 60 degree angle given as 120°.

Formula for the circumference of a circle is;

C = 2πr

C = 50π inches

C = 157 inches

The arc made by the 50° angle is;

Arc length = 157*100/360

=  43.6 inches

The arc length made by the 60° angle = 157(120/360)

=  52.3 inches

The arc length made by the remaining 70° angle is;

Arc length = 157(140/360)

Arc length = 61.1 inches

Total arc length = 43.6 + 52.3 + 61.1

= 157 inches.

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Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case we have

268 = 2×86 + 2x = 172 + 2x

96 = 2x

x = 96/2 = 48 m

The key is to check whether the given side measures satisfy the triangle inequality theorem or not, if yes then we can create a unique triangle, if no then no triangle can be created, and if the given measures are the perimeter of a triangle, we can create many triangles.

When given three side measures of a triangle, the following scenarios can occur:

Unique triangle: If the three side measures given are the lengths of the three sides of a triangle and they satisfy the triangle inequality theorem, then we can create a unique triangle. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

No triangle: If the three side measures given do not satisfy the triangle inequality theorem, then it is not possible to create a triangle with those side lengths.

Many triangles: If the three side measures given are the perimeter of a triangle, and we are allowed to vary the lengths of the three sides of the triangle within a certain range, then we can create infinitely many triangles.

Example: A triangle with perimeter 12cm, we can create a unique triangle with sides 3,4,5, or we can create many triangle with sides (2,5,5), (4,4,4),(3,4,5) and so on.

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Answer:

50%

Step-b50%y-step explanation:

Joint relative frequency

Isosceles Triangle Theorem: If two triangle sides are similar, then their corresponding angles must also be similar. The sides of a triangle that correspond to two angles that are congruent are also congruent.

According to the isosceles Angle Theorem, the angles in an isosceles triangle that face congruent sides are also congruent.

A triangle with two equal sides is said to be isosceles. Isosceles triangle is basically such triangle which have two sides equal in magnitude. It is to be noted that because two angles should also be equal because of the two equal sides.

Angles opposing two triangle sides are congruent if their two sides are as well.

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Answer:

5x + 7y + 4

Step-by-step explanation:

5x + (6y+y) ( 3+1)

5x + 7y + 4

The value of x for the given angles is 23

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. The angles that result from a transversal crossing of two lines in pairs can be successive internal angles, matching angles, or alternate angles.

Given lines m and n, where m ║ n

and t intersect at both the lines as shown in the figure,

so line t works s transversal,

and angles,

(8x - 27)° and (7x - 4)°

both the angles are at the bottom of the line and same side so they are corresponding angles,

and corresponding angles for any transversal are equal,

(8x - 27)° = (7x - 4)°

8x - 27 = 7x - 4

8x - 7x = -4 + 27

x = 23

Hence the value of x is 23.

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The radian measure of an angle theta is the length of the arc that subtended angle 2Pi

We can measure angle in two form degrees or Radian.

What is the meaning of radian?

Radian can be described as a measure of angle subtended by a circular arc. It can be defined as the ratio of the arc length subtending angle to the radius of circle.

One radian is the measure of angle subtended by by an arc that is equal to the radius of circle.

Therefore,the radians measure an angle theta the length of arc.

Θ =s/r ,

where, theta is the angle subtended, s is the arc length and r is the radius of circle.

We know that the 2π radians = 360 degrees.

That subtends the angle in a circle of radius 2Pi

Therefore ,The radian measure of an angle theta is the length of the arc that subtended angle 2 Pi

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According to Maths, in order to solve a system of linear equations by graphing, we must first graph both equations in the same coordinate plane and then locate the intersection of the two lines.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables. An illustration of a system of equations is the set of equations below.

2x - y = 12

x - 2y = 48

Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions,

There are numerous ways to solve any set of equations. We require at least two equations in order to solve a system of two-variable equations. Similar to this, we will need at least 3 equations to solve a system of 3 equations. Let's examine three approaches to solving a set of equations, presuming that they are linear equations in two variables.

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Check the picture below.

The revised form of the sentence would be as follows: Mark Twain, who was born in Florida, is one of America's most famous authors.

Nonrestrictive elements are sets of words that can be deleted from a statement without affecting its meaning.

A nonrestrictive element is nonessential because we don't need the information it provides. These elements are always separated with commas from the rest of the sentence to specify that they are not essential. If they were dropped, the meaning of the sentence would be left unchanged.

Mark Twain, is one of America's most famous authors. - In the above sentence the nonrestrictive element is a nonessential relative clause.

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To determine the x-intercept, solve for x while replacing y with 0. To obtain the y-intercept, solve for y while replacing x with 0.

( 3, 0 ) are the x-intercepts.

(0, 6) are the y-intercepts.

6. Y-intercept In order to find x, set x = 0 in the equation y = 2x - 6. It is -6 for the y-intercept. By selecting "New Example" below, you may read some additional examples.

The Y-value of every point 6 units below the X-axis is actually equal to -6. As a result, the plane's points that are 6 units below the X-axis form the graph of y = -6.

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A square's side to perimeter ratio is one to four.

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Answer:

$389.5

Step-by-step explanation:

621/2 = 310.5 assuming they're equal therefore, it is stated that the table cost cost 79 less than the bench so we substract.

310.5 - 79 = 231.5

This is the cost of garden table, lets find the bench now.

621(both table and bench)-231.5(garden table)= 389.5 is the cost of the bench.

Answer:

218 with a remainder of 2

Step-by-step explanation:

656 divided by 3 = 218.6666667

218 times 3 = 654

656 - 654 = 2

When 656 is divided by 3 is 218 with a remainder of 2.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To divide 656 by 3, we can perform long division as follows:

 3 ) 656 (218

     -6

     ____

     15

    -12

   _____

      35

    - 33

    _____

       2

We first divide the first digit of 656 (which is 6) by the divisor 3, which gives us 6 with a remainder of 15.

We then bring down the next digit (which is 56) to form the dividend 18, and we perform the division again.

This gives us 218 with a remainder of 2.

Therefore, 656 divided by 3 is 218 with a remainder of 2.

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A ruler and a pencil may be used to quickly create the triangle XYZ.

The length of the sides and the angle of the triangle XYZ are the fundamental concepts needed to start.

The steps to design a triangle whose three sides are known are as follows:

1. Mark point A, which will serve as one of the triangle's vertices.

2. Set the required length AB for the compass breadth.

3. Cut an arc by setting the compass's width to the required length of the side AC.

4. Cut an arc by setting the compass's width to the appropriate length of side BC.

You may thus obtain the needed triangle.

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Answer:40+4x

Step-by-step explanation:

1) distribute the 4 to each term

4(10+x)

40+4x